It was shown in [1]} that the SGF is related to the high-temperature expansion of the Ising model defined on the same tetrahedron graph. In fact, such a relation can be
generalized to an arbitrary three-valent planar graph (with the Kasteleyn orientation).
Explicitly, the scaleless spin network evaluation, as a function of the spinors, is inversely proportional to the square of the amplitude \(Z^{\text{Ising}}_{\Gamma }\) , as a function of the edge couplings \(\lbrace Y_l\rbrace \)  in terms of the spinors \(\lbrace z_l,\tilde{z}_l\rbrace \) , of the Ising model, which is a polynomial of the couplings. Precisely,
\({\mathcal {S}}^{\text{sl}}_\Gamma (\lbrace z_l,\tilde{z}_l\rbrace ) =\left( 2^{2|N|} \prod _{e\in \Gamma } \cosh ^2 y_l \right) {\left[Z^{\text{Ising}}_\Gamma (\lbrace y_l\rbrace )\right]^2}\,, \quad \text{ with }\quad Z^{\text{Ising}}_\Gamma (\lbrace y_l\rbrace ) = \sum _{{\mathcal {L}}\in \Gamma } \prod _{l\in {\mathcal {L}}} \tanh y_l\,,\) 
